Laura,
I've been travelling with a dSLR for the last few years, as photography is an important component of my travels. Despite the size and weight, I will continue to haul my Camera gear around Europe. I use Canon gear, so not familiar with the Sony products. You might also have a look at the new T2i.
I'd highly recommend buying the dSLR ASAP, so that you can become somewhat familiar with it. There is definitely a "learning curve" with that type of Camera, and in order to get the best results you'll need to have some idea how it works.
Memory Cards are relatively cheap at the moment, so be sure to have enough for "reasonable" storage capacity. The capacity will depend somewhat on your "shooting style" and Camera settings. For example, shooting RAW + JPEG creates fairly large file sizes for each photo, so larger memory cards are a good idea. If you just want "snapshots", then using JPEG only is fine (each compressed image will be ~3-4 MB, so you'll be able to fit lots on a card). With a dSLR I wouldn't use anything less than a 4GB card.
The subject of backup storage for photos during travel is always a hotly debated topic here on the HelpLine. Everyone seems to have a preferred method. My preference is to use multiple Memory Cards as well as some form of backup storage. I've also decided to travel with a Netbook this year (for the first time). The 250GB HD will provide lots of storage capacity.
As each Memory Card is filled, I back it up and then store the card in a "safe" location (separate from the Camera). That way I have both the backup images on the HD as well as the original card. I have enough cards that I can usually last for the trip without having to re-use the Card. However my trip this year will be longer, so will have to see if I can use the same method this time.
I'll also be in Greece and the islands in May & June (among other locations).
Finally, congratulations!